CONTROLLERS FOR MULTICHANNEL FEEDFORWARD CONTROL OF STOCHASTIC DISTURBANCES

摘要

A time domain formulation for the multichannel feedforward control problem (Figure 1) is used to derive an optimality condition for the least squares controller. It is also used to motivate an instantaneous steepest descent algorithm for the adaptation of the controller, which is the (known) filtered error LMS algorithm (Figure 2). The convergence rate of this algorithm is limited by the correlation properties of each reference signal, their cross-correlation properties and the dynamics and coupling within the plant response. An expression is then derived for the transfer function of the optimum least squares controller. A new architecture (Figure 3) for the adaptive controller whose convergence rate is not limited by the factors mentioned above is described. A set of white and uncorrelated reference signals are generated to drive a modified matrix C(z) of control filters, whose outputs are multiplied by the inverse of the minimum phase part G-1min(z) of the plant response matrix G(z) before being fed to the physical plant. The error signals e(n) from the plant are then used to update this controller after being fed through the time-reverse transpose z-J GTall(Z-1) of the all-pass part of the plant matrix.